8. The coordinates of an object moving in R³ at time t are x = t, y = t², z = (2/3)t³. What is the distance traveled by the object between t = 0 and t = 3 ?

The distance traveled by the object between t = 0 and t = 3 is given by the length of the arc created by the object in R³ from t = 0 to t = 3.

The length, L, of an arc in R³ from t = a to t = b is given by,

Since

the distance traveled by the object is,